Simplify (x^4y^-8z^-2)/(x^-1y^6z^-10)

$\frac{x^{4} y^{- 8} z^{- 2}}{x^{- 1} y^{6} z^{- 10}}$

Step 1

Move $y^{- 8}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{x^{4} z^{- 2}}{x^{- 1} y^{6} z^{- 10} y^{8}}$

Step 2

Multiply $y^{6}$ by $y^{8}$ by adding the exponents.

Move $y^{8}$ .

$\frac{x^{4} z^{- 2}}{x^{- 1} (y^{8} y^{6}) z^{- 10}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x^{4} z^{- 2}}{x^{- 1} y^{8 + 6} z^{- 10}}$

Add $8$ and $6$ .

$\frac{x^{4} z^{- 2}}{x^{- 1} y^{14} z^{- 10}}$

Step 3

Move $x^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{x^{4} z^{- 2} x}{y^{14} z^{- 10}}$

Step 4

Move $z^{- 10}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{x^{4} z^{- 2} x z^{10}}{y^{14}}$

Step 5

Simplify the numerator.

Multiply $x^{4}$ by $x$ by adding the exponents.

Move $x$ .

$\frac{x \cdot x^{4} z^{- 2} z^{10}}{y^{14}}$

Multiply $x$ by $x^{4}$ .

Raise $x$ to the power of $1$ .

$\frac{x^{1} x^{4} z^{- 2} z^{10}}{y^{14}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x^{1 + 4} z^{- 2} z^{10}}{y^{14}}$

Add $1$ and $4$ .

$\frac{x^{5} z^{- 2} z^{10}}{y^{14}}$

Multiply $z^{- 2}$ by $z^{10}$ by adding the exponents.

Move $z^{10}$ .

$\frac{x^{5} (z^{10} z^{- 2})}{y^{14}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x^{5} z^{10 - 2}}{y^{14}}$

Subtract $2$ from $10$ .

$\frac{x^{5} z^{8}}{y^{14}}$